A Note on Weighted Rooted Trees

Let $T$ be a tree rooted at $r$. Two vertices of $T$ are related if one is a descendant of the other; otherwise, they are unrelated. Two subsets $A$ and $B$ of $V(T)$ are unrelated if, for any $a\in A$ and $b\in B$, $a$ and $b$ are unrelated. Let $\omega$ be a nonnegative weight function defined on $V(T)$ with $\sum_{v\in V(T)}\omega(v)=1$. In this note, we prove that either there is an $(r, u)$-path $P$ with $\sum_{v\in V(P)}\omega(v)\ge \frac13$ for some $u\in V(T)$, or there exist unrelated sets $A, B\subseteq V(T)$ such that $\sum_{a\in A }\omega(a)\ge \frac13$ and $\sum_{b\in B }\omega(b)\ge \frac13$. The bound $\frac13$ is tight. This answers a question posed in a very recent paper of Bonamy, Bousquet and Thomass\'e

Is Labor Green?

In this article, we assess whether unionization of national workforces influences growth in national carbon dioxide (CO2) emissions per capita. Political-economic theories in environmental sociology propose that labor unions have the potential to affect environmental conditions. Yet, few studies have quantitatively assessed the influence of unionization on environmental outcomes using cross-national data. We estimate multilevel regression models using data on OECD member nations from 1970 to 2014. Results from our analysis indicate that unionization, measured as the percentage of workers who are union members, is negatively associated with CO2 emissions per capita, even when controlling for labor conditions. This finding suggests that unionization may promote environmental protection at the national level

Cross-Identification Performance from Simulated Detections: GALEX and SDSS

We investigate the quality of associations of astronomical sources from multi-wavelength observations using simulated detections that are realistic in terms of their astrometric accuracy, small-scale clustering properties and selection functions. We present a general method to build such mock catalogs for studying associations, and compare the statistics of cross-identifications based on angular separation and Bayesian probability criteria. In particular, we focus on the highly relevant problem of cross-correlating the ultraviolet Galaxy Evolution Explorer (GALEX) and optical Sloan Digital Sky Survey (SDSS) surveys. Using refined simulations of the relevant catalogs, we find that the probability thresholds yield lower contamination of false associations, and are more efficient than angular separation. Our study presents a set of recommended criteria to construct reliable cross-match catalogs between SDSS and GALEX with minimal artifacts.Comment: 7 pages, 9 figures; ApJ in pres

The Clustering of AGN in the Sloan Digital Sky Survey

We present the two--point correlation function (2PCF) of narrow-line active galactic nuclei (AGN) selected within the First Data Release of the Sloan Digital Sky Survey. Using a sample of 13605 AGN in the redshift range 0.055 < z < 0.2, we find that the AGN auto--correlation function is consistent with the observed galaxy auto--correlation function on scales 0.2h^{-1}Mpc to >100h^{-1}Mpc. The AGN hosts trace an intermediate population of galaxies and are not detected in either the bluest (youngest) disk--dominated galaxies or many of the reddest (oldest) galaxies. We show that the AGN 2PCF is dependent on the luminosity of the narrow [OIII] emission line (L_{[OIII]}), with low L_{[OIII]} AGN having a higher clustering amplitude than high L_{[OIII]} AGN. This is consistent with lower activity AGN residing in more massive galaxies than higher activity AGN, and L_{[OIII]} providing a good indicator of the fueling rate. Using a model relating halo mass to black hole mass in cosmological simulations, we show that AGN hosted by ~ 10^{12} M_{odot} dark matter halos have a 2PCF that matches that of the observed sample. This mass scale implies a mean black hole mass for the sample of M_{BH} ~ 10^8 M_{odot}.Comment: 5 pages, 4 figures. Accepted for publication in ApJ

Quasi-Gorenstein Modules

This thesis will study the various roles that quasi-Gorenstein modules and their properties play in the study of homological dimensions and linkage of modules. To that effect we begin by studying these modules in their own right. An R-module M of grade g will be quasi-Gorenstein if ExtiR(M, R) = 0 for i 6= g and there is an isomorphism M ∼= ExtgR(M, R). Such modules have many nice properties which we will explore throughout this thesis. We will show they help extend a characterization of diagonalizable matrices over principal ideal domains to more general rings. We will use their properties to help lay a foundation for a study of homological dimensions, helping to generalize the concept of Gorenstein dimension to modules of larger grade and present a connection to these new dimensions with certain generalized Serre conditions. We then give a categorical construction to the concept of linkage. The main motivation of such a construction is to generalize ideal and module linkage into one unified theory. By using the defintion of linkage presented by Nagel [53], we can use categorical language to define linkage between categories. One of the focuses of this thesis is to show that the history of linkage has been wrought with a misunderstanding of which classes of objects to study. We give very compelling evidence to suggest that linkage is a tool to gain information about the even linkage classes of objects. Further, scattered among the literature is a wide array of results pertaining to module linkage, homological dimensions, duality, and adjoint functor pairs and for which we show that these fall under the umbrella of this unified theory. This leads to an intimate relationship between associated homological dimensions and the linkage of objects in a category. We will give many applications of the theory to modules allowing one to cover vast grounds from Gorenstein dimensions to Auslander and Bass classes to local cohomology and local homology. Each of these gives useful insight into certain classes of modules by applying this categorical approach to linkage

Comparing the 2013 ACC/AHA & 2014 NLA Dyslipidemia Guidelines and Their Impact on Clinical Decision Making

This home-study CPE activity has been developed to educate pharmacists on the similarities and differences between the 2014 NLA Recommendations for Dyslipidemia Management and the 2013 ACC/AHA Guidelines for Treatment of Blood Cholesterol

Cross-Identification of Stars with Unknown Proper Motions

The cross-identification of sources in separate catalogs is one of the most basic tasks in observational astronomy. It is, however, surprisingly difficult and generally ill-defined. Recently Budav\'ari & Szalay (2008) formulated the problem in the realm of probability theory, and laid down the statistical foundations of an extensible methodology. In this paper, we apply their Bayesian approach to stars that, we know, can move measurably on the sky, with detectable proper motion, and show how to associate their observations. We study models on a sample of stars in the Sloan Digital Sky Survey, which allow for an unknown proper motion per object, and demonstrate the improvements over the analytic static model. Our models and conclusions are directly applicable to upcoming surveys such as PanSTARRS, the Dark Energy Survey, Sky Mapper, and the LSST, whose data sets will contain hundreds of millions of stars observed multiple times over several years.Comment: 10 pages, 5 figure

NHANES-GCP: Leveraging the Google Cloud Platform and BigQuery ML for reproducible machine learning with data from the National Health and Nutrition Examination Survey

Summary: NHANES, the National Health and Nutrition Examination Survey, is a program of studies led by the Centers for Disease Control and Prevention (CDC) designed to assess the health and nutritional status of adults and children in the United States (U.S.). NHANES data is frequently used by biostatisticians and clinical scientists to study health trends across the U.S., but every analysis requires extensive data management and cleaning before use and this repetitive data engineering collectively costs valuable research time and decreases the reproducibility of analyses. Here, we introduce NHANES-GCP, a Cloud Development Kit for Terraform (CDKTF) Infrastructure-as-Code (IaC) and Data Build Tool (dbt) resources built on the Google Cloud Platform (GCP) that automates the data engineering and management aspects of working with NHANES data. With current GCP pricing, NHANES-GCP costs less than $2 to run and less than$15/yr of ongoing costs for hosting the NHANES data, all while providing researchers with clean data tables that can readily be integrated for large-scale analyses. We provide examples of leveraging BigQuery ML to carry out the process of selecting data, integrating data, training machine learning and statistical models, and generating results all from a single SQL-like query. NHANES-GCP is designed to enhance the reproducibility of analyses and create a well-engineered NHANES data resource for statistics, machine learning, and fine-tuning Large Language Models (LLMs). Availability and implementation" NHANES-GCP is available at https://github.com/In-Vivo-Group/NHANES-GCPComment: 7 pages, 1 figur